To add to what Zooey explained...
To sweep is to use a broom to scrape the floor and push all the dirt to one side. "Swept" is past tense of "to sweep". The dirt was swept up by the broom, and you were swept by the excitement so you went to dance like all the other people.
When you say you were "swept up" by something, it means that you let yourself go, to experience the moment, and feel the full force of it. You can be swept up in the movie and cry for the main character. Or you can be swept up by the strong emotions of an election, or sporting event, or birth of a child, etc.